Homogenization and multigrid

N. Neuss*, W. Jäger, Gabriel Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

For elliptic partial differential equations with periodically oscillating coefficients which may have large jumps, we prove robust convergence of a two-grid algorithm using a prolongation motivated by the theory of homogenization. The corresponding Galerkin operator on the coarse grid turns out to be a discretization of a diffusion operator with homogenized coefficients obtained by solving discrete cell problems. This two-grid method is then embedded inside a multi-grid cycle extending over both the fine and the coarse scale.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalComputing (Vienna/New York)
Volume66
Issue number1
DOIs
StatePublished - Jul 17 2001

Keywords

  • Block smoothers
  • Homogenization
  • Multigrid
  • Multilevel methods
  • Oscillating coefficients
  • Partial differential equations
  • Robustness

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics

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